Multistation observations of the azimuth, polarization, and … · RadioScience 10.1002/2015RS005683 0 0.5 1 0 0.5 1 0.92 0.94 0.96 0.98 Normalized Magnitude of Horizontal Magnetic

Radio Science

Multistation observations of the azimuth, polarization,and frequency dependence of ELF/VLF wavesgenerated by electrojet modulation

A. S. Maxworth1, M. Gołkowski1, M. B. Cohen2, R. C. Moore3, H. T. Chorsi1, S. D. Gedney1,and R. Jacobs1

1Department of Electrical Engineering, University of Colorado Denver, Denver, Colorado, USA, 2School of Electrical andComputer Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA, 3Department of Electrical and ComputerEngineering, University of Florida, Gainesville, Florida, USA

Abstract Modulated ionospheric heating experiments are performed with the High Frequency ActiveAuroral Research Program facility in Gakona, Alaska, for the purpose of generating extremely low frequency(ELF) and very low frequency (VLF) waves. Observations are made at three different azimuths from theheating facility and at distances from 37 km to 99 km. The polarization of the observed waves is analyzed inaddition to amplitude as a function of modulation frequency and azimuth. Amplitude and eccentricity areobserved to vary with both azimuth and distance from the heating facility. It is found that waves radiated atazimuths northwest of the facility are generated by a combination of modulated Hall and Pedersen currents,while waves observed at other azimuths are dominated by modulated Hall currents. We find no evidencefor vertical currents contributing to ground observations of ELF/VLF waves. Observed amplitude peaks nearmultiples of 2 kHz are shown to result from vertical resonances in the Earth-ionosphere waveguide, andvariations of the frequency of these resonances can be used to determine the D region ionosphere electrondensity profile in the vicinity of the HF heater.

1. Introduction

It is a significant engineering challenge to effectively radiate extremely low frequency (ELF: 3 Hz–3 kHz)and very low frequency (VLF: 3 kHz–30 kHz) electromagnetic waves. The free space wavelengths at thesefrequencies are on the order of tens to hundreds of kilometers, making it difficult to construct an antenna ofappreciable electrical length. Even if a very long horizontal antenna is constructed, radiation in the ELF bandis impeded by image currents along the Earth’s surface, which is a good conductor at such low frequencies.Since both the surface of the Earth and the ionosphere are conductive, ELF/VLF radiation is effectively guidedaround the globe in the so-called Earth-ionosphere waveguide, which can be approximated as a parallelplate waveguide with a separation of approximately 70–85 km. The unique global propagation capabilityand a skin depth of at least several meters in both seawater and the ground make the ELF/VLF band of con-tinued engineering interest despite the low data rates (or equivalently narrow bandwidths) associated withthese frequencies.

Starting from the early 1970s, physicists and engineers have engaged in active experiments to modify theionosphere with high-power high-frequency (HF: 1–10 MHz) radio waves [Getmantsev et al., 1974]. Heatingthe ionosphere with HF waves can change the electron temperature and therefore the collision frequencywithin the D region ionosphere which is a key parameter in the plasma conductivity tensor. In the presenceof natural ionospheric currents (like the auroral electrojet or equatorial electrojet), periodic modulation ofthe electron temperature at frequencies in the ELF/VLF band can be used to transform the ionosphere into avirtual antenna [Stubbe et al., 1981, 1982; Barr and Stubbe, 1984a, 1984b].

A significant number of ELF/VLF generation experiments have been conducted at different ionospheric heat-ing facilities. At the Arecibo Observatory in Puerto Rico and at the Jicamarca Observatory in Peru HF facilitieswere used to generate weak ELF signals with the equatorial electrojets [Ferraro et al., 1982; Lunnen et al.,1984]. The European Incoherent Scatter facility located in Tromsø, Norway, the High Frequency Active AuroralResearch Program (HAARP), and the Sura ionospheric heating facility in Russia have been extensivelyutilized for the modulation of auroral electrojets [Stubbe et al., 1981; Barr and Stubbe, 1991; Moore et al., 2007;

RESEARCH ARTICLE10.1002/2015RS005683

Key Points:• Collisional heating is the

dominant process in D regionelectrojet modulation

• There is an azimuthal dependence tothe HAARP-induced ELF/VLF source

• Vertical resonances cause amplitudeenhancements near multiple of 2 kHz

Correspondence to:A. S. Maxworth,[email protected]

Citation:Maxworth, A. S., M. Gołkowski,M. B. Cohen, R. C. Moore, H. T. Chorsi,S. D. Gedney, and R. Jacobs (2015),Multistation observations of theazimuth, polarization, and fre-quency dependence of ELF/VLFwaves generated by electrojet mod-ulation, Radio Sci., 50, 1008–1026,doi:10.1002/2015RS005683.

Received 19 FEB 2015

Accepted 9 SEP 2015

Accepted article online 11 SEP 2015

Published online 7 OCT 2015

©2015. American Geophysical Union.All Rights Reserved.

MAXWORTH ET AL. MULTISTATION ELF OBSERVATIONS 1008

http://publications.agu.org/journals/

http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1944-799X

http://dx.doi.org/10.1002/2015RS005683

Radio Science 10.1002/2015RS005683

Fujimaru and Moore, 2011; Cohen et al., 2012; Gołkowski et al., 2011; Cohen and Golkowski, 2013; Kotik et al.,2013]. The two main modes of heating the ionosphere are called the ordinary mode (O mode) and the extraor-dinary mode (X mode). For the case of ionospheric current modulation in the D and lower E region ionosphereat subauroral latitudes where the HF carrier frequency is much greater than the local plasma frequency, thesetwo modes are essentially left- and right-hand circularly polarized modes, respectively.

There are at least three major classes of techniques that have been investigated to modulate ionosphericcurrents at ELF/VLF frequencies. The first and simplest method is amplitude modulation, where the HF carrieris ON/OFF modulated (usually 50% duty cycle square wave). The unique flexibility of the HAARP ionosphericheating facility has allowed for more sophisticated modulation techniques to be explored. In the secondmethod known as beam painting [Papadopoulos et al., 1990], the HF carrier frequency is still ON/OFFmodulated but the HF beam is not in a fixed stationary position. Instead, during the ON portion, the beamis quickly scanned over an area much larger than the beam width and at a rate faster than the cooling rateof the electrons. The third method is geometric modulation [Barr et al., 1987; Cohen et al., 2008b], where theHF beam is always ON (CW) and moved along a geometric pattern at a rate equal to the ELF/VLF modu-lation frequency. Amplitude modulation and continuous wave modulation techniques were compared byBarr and Stubbe [1997], and all three techniques are experimentally compared by Cohen et al. [2010b].Additional approaches to ELF/VLF generation independent of the ionospheric currents include the so-calledionospheric current drive [Papadopoulos et al., 2011] and cubic nonlinearity [Kotik and Ermakova, 1998;Moore et al., 2013].

We focus on amplitude modulation as this is the most common technique and also most readily realizedat all ionospheric modification facilities including the planned heater at the Arecibo Observatory. Severalkey features of ionospherically generated ELF/VLF waves have been documented. From the time of the firstexperiments it was found that the amplitudes of generated ELF/VLF signals exhibit maxima near multiplesof 2 kHz [Stubbe et al., 1982; Papadopoulos et al., 2003; Cohen et al., 2012]. This has been attributed to eithervertical resonances of the Earth-ionosphere waveguide [Stubbe et al., 1982] or as a result of optimal electronheating and cooling rates at these frequencies [Papadopoulos et al., 2003]. Time of arrival analysis performedby Fujimaru and Moore [2011] illustrated that the typical source currents are located at altitudes of 70–80 km,consistent with earlier studies [e.g., Rietveld et al., 1989]. Cohen et al. [2008a] demonstrated that at distancesapproaching 1000 km, in what can be called the far field, the current source is well approximated by a dipoleoriented in the direction of the Hall current. The dependence of the generated signal strength has been shownto be a function of not only the electrojet currents but also the D region electron profile [Jin et al., 2011; Agrawaland Moore, 2012].

Most previous works used observations at a single site and not at multiple sites. Consequently, the azimuthaldependence of the radiated waves has not been fully explored. Furthermore, the dominant focus of previouswork has been on observed amplitude with much less analysis of the observed wave polarization, includingits elliptical nature. In this context, it is also not clear which currents (Hall, Pedersen, or geomagnetically fieldaligned) are most responsible for observations in the near field (<150 km from the heating facility) and atwhat minimum distances the single dipole model of Cohen et al. [2008a] can be assumed to be valid [Payne,2007; Payne et al., 2007].

Here we present multiple site observations of the amplitude and polarization as a function of modulationfrequency. The organization is as follows: section 2 describes the experiment. Observations are described andanalyzed in section 3. In the fourth section we compare our observations with simulations of the ionosphericHF heating process. Discussion of the results and general conclusions are presented in the final section.

2. Experiment

The experiment was carried out with the HAARP facility located in Gakona, Alaska, during several days of theHAARP Student Summer Research Campaign in July 2011. In this experiment the HF beam was directed verti-cally and was modulated using square wave amplitude modulation with a carrier frequency of 2.75 MHz. Thepolarization of the HF heating beam alternated between X and O mode. The transmission sequence consistsof 40 frequency tones chosen to avoid local power line harmonics.The exact values of the frequency tones aregiven in Table 1; details of the experiment times are shown in Table 2. Each tone was transmitted for 1 s. Thetotal duration for the format (including a 20 s frequency-time ramp not discussed here) was 60 s. This pattern



Table 1. Exact Values of the Frequency Tones in Hertz

Frequency Tones (Hz)

500 2500 4525 6500

700 2725 4700 6700

925 2900 4900 6925

1100 3100 5125 7100

1300 3325 5300 7300

1525 3500 5500 7525

1700 3700 5725 7700

1900 3925 5900 7900

2125 4100 6100 8125

2300 4300 6325 8300

was repeated 5 times for X mode and 5 times forO mode for approximately 30 min several timesbetween 19 July 2011 and 25 July 2011. Figure 1ashows an observed spectrogram where the tonesand ramp of the format are clearly visible.

Observations were made at three sites locatedwithin 100 km of HAARP as shown in Figure 1b.The magnetic declination at the HAARP site is21.65∘. The sites are Chistochina (36 km distance,geographic azimuth: 47.7∘, geomagnetic azimuth:26.05∘), Paxson (52 km distance, geographicazimuth: −20∘, geomagnetic azimuth: −41.65∘)and Paradise (99 km distance, geographic azimuth:80.3∘, geomagnetic azimuth: 58.65∘) with respectto the HAARP facility. Signals at all sites were

recorded using ELF/VLF receivers with orthogonal air core loop antennas oriented perpendicular to theground. The receivers at Chistochina and Paxson are of the same type as described by Cohen et al. [2010a].

3. Observations3.1. Frequency Dependence of AmplitudesThe amplitudes of the received signals were analyzed as a function of the ELF modulation frequency. Trans-missions using X mode yielded ELF/VLF amplitude 3–10 dB higher than O mode transmissions with all otherfeatures being approximately the same as can be seen in Figure 2, which shows the observed field magnitudesfor the three sites, for X mode and O mode on 21 July 2011, 5:30 UT, normalized to the maximum observedvalue. Therefore, subsequent discussion here refers only to X mode transmissions. The observed calibratedmagnitudes for all three sites are shown in Figure 3 as a function of frequency. Range bars indicate the stan-dard deviation from the mean. Figure 3a shows data from 21 July 2011, 05:30 UT during which the strongestwaves were observed. Figure 3b shows the observations for transmissions 3 h later, while Figure 3c shows theaveraged amplitude over 6 days of transmissions. The magnitude at each site is the overall horizontal mag-netic field magnitude, in other words, the square root of the sum of the squares of the amplitudes from thetwo antennas.

Focusing on Figure 3a, it can be seen that the highest amplitude is observed at a modulation frequency of2.125 kHz for all three sites in line with that observed in previous work [Stubbe et al., 1982; Papadopoulos et al.,2003; Cohen et al., 2012]. However, after the first peak observed at 2.125 kHz at all sites, the next highest peaksobserved at Chistochina and Paxson are at 4.3 kHz and 6.325 kHz. The amplitudes observed at Paradise actuallyexhibit minima at 4.1 kHz and 6.325 kHz, and peaks shifted slightly to higher frequencies near 4.525 kHz and7.1 kHz. We see this difference in the frequency response near 4 kHz and 6 kHz between Paradise, and the othertwo sites is strong evidence that the amplitude peaks are a result of the Earth-ionosphere waveguide ratherthan the generation process as suggested by Papadopoulos et al. [2003]. Furthermore, we interpret the shift ofthe peaks in frequency at Paradise to be indicative of a transition from locally resonant modes to propagatingmodes in the Earth-ionosphere waveguide. Namely, vertical resonances in the Earth-ionosphere waveguide

Table 2. Experiment Times and Solar Zenith Angles

Experiment Conditions

Day UT MLT Solar Zenith Angle

19 July 2011 9.02–9.29 19.02–19.29 97.26∘

20 July 2011 6.30–6.59 16.30–16.59 88.64∘

21 July 2011 5.30–5.59 15.30–15.59 83.33∘

21 July 2011 8.30–8.59 18.30–18.59 96.85∘

22 July 2011 9.02–9.29 19.02–19.29 97.82∘

23 July 2011 10.10–10.40 20.10–20.40 98.56∘

24 July 2011 5.30–5.59 15.30–15.59 83.86∘



(a)

(b)

Figure 1. (a) Spectrogram of HF transmission format observed at Chistochina for a duration of 1 min. Both thefundamentals and the harmonics of the generated ELF/VLF tones are visible in the figure. (b) Location of the three siteswith respect to HAARP. Note that the Paxson site referred to here is considerably south of the geographic place namePaxson located at the junction of the Richardson and Denali highways. GN: geographic north and MN: magnetic north.

are expected to occur when the distance between the conducting ground and the conducting ionosphere areequal to a multiple of half a wavelength, while propagating modes are governed by cutoff frequencies andassociated conductive losses. This identification of resonant versus propagating modes in the observations isa key conclusion of the present work, and we therefore justify our interpretation with theoretical considerationof a parallel waveguide as an approximation to the Earth-ionosphere waveguide as described below.3.1.1. Analytical and Numerical Analysis of Resonant Versus Propagating ModesThe complex phaser amplitudes of the electric, E, and magnetic, H, fields in a parallel plate waveguide withperfectly conducting plates in the x-y plane can be written as [Inan and Inan, 1999, chap. 4]

Ey = E0 sin(m𝜋

h

)e−𝛾x (1)



0 1 2 3 4 5 6 7 8 90

0.5

1

Frequency (kHz)

Nor

mal

ized

Am

plitu

de

Chistochina X modeChistochina O mode

0 1 2 3 4 5 6 7 8 90

0.5

1

Frequency (kHz)

Nor

mal

ized

Am

plitu

de

Paxson X modePaxson O mode

0 1 2 3 4 5 6 7 8 90

0.5

1

Frequency (kHz)

Nor

mal

ized

Am

plitu

de

Paradise X modeParadise O mode

Figure 2. Normalized amplitudes for X mode and O mode transmissions for all three sites on 21 July 2011 averaged over5 min (5:30 UT–5:35 UT).

Hx =jm𝜋

𝜔𝜇0hE0 cos

(m𝜋

hz)

e−𝛾x (2)

Hz = 0 (3)

for transverse electric (TE) modes and

Hy = 𝜔𝜖hjm𝜋

E0 cos(m𝜋

h

)e−𝛾xe−𝛾x (4)

Ex = E0 sin(m𝜋

hz)

e−𝛾x (5)

Ez = 0 (6)

for transverse magnetic (TM) modes where E0 is the arbitrary amplitude of the electric field, h is the plate

separation, m is the mode number, and 𝛾 =√(

m𝜋

h

)2− 𝜔2𝜇0𝜖0 is the complex propagation constant for

assumed propagation in the x direction. The conditions for vertical resonance are the same as for cutoff in that𝛾 = 0, and there is no distinction between TE and TM modes if anisotropy of the medium is neglected. Withoutloss of generalization, we consider the TE mode only. The width of the resonant peaks can be obtained fromthe effective quality factor Q of this vertical cavity and using the universal resonance formulation [Siebert,1986, p. 113]

|Hx(f )| ∝ 1

1 + 4Q2

f 2m

(f − fm

)2(7)



0 1 2 3 4 5 6 7 8 90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Frequency(kHz)

Am

plitu

de(p

T)

ChistochinaPaxsonParadise4.3kHz

6.325kHz

7.1kHz

2.125kHz

4.525kHz

0 1 2 3 4 5 6 7 8 90

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Frequency(kHz)

Am

plitu

de(p

T)

ChistochinaPaxsonParadise

2.125kHz 4.1kHz

6.1kHz

7.1kHz4.9kHz

0 1 2 3 4 5 6 7 8 90

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Frequency(kHz)

Am

plitu

de(p

T)


(a)

(b)

(c)

Figure 3. Magnitude versus frequency graphs for the three sites on (a) 21 July 2011 at 5.30 UT averaged over 5 min(5.30 UT–5.35 UT), (b) 21 July 2011 at 8.40 UT averaged over 5 mins (8.40 UT–8.45 UT), (c) averaged over 6 days (19 July2011 to 24 July 2011). Range bars show standard deviation from the observed mean magnitude.



0 2 4 6 80

0.2

0.4

0.6

0.8

1

Frequency (kHz)

Nor

mal

ized

Am

plitu

de

Expected Vertical Resonance Peaks

Figure 4. Normalized magnitude for vertical Earth-ionosphere resonances assuming reflection at altitude of 71.5 kmwith ionospheric conductivity of 0.09 mS/m.

where fm is resonance frequency or cutoff frequency of mode order m. The Q of the vertical Earth-ionosphereresonator can be calculated using the average stored energy, Wstr, in the fields and the power loss, Ploss, fromreflection at the Earth and ionospheric boundaries [Inan and Inan, 1999, chap. 5] as follows

Q = 2𝜋fm

Wstr

Ploss= 𝜋fm

𝜖0 ∫V |Ey|2dv + 𝜇0 ∫V |Hx|2dv

Ris ∫iono |Hy|2ds + RE

s ∫Earth |Hy|2ds(8)

where REs and Ri

s are the surface resistances of the Earth and ionosphere, respectively, given by Rs =√𝜋f𝜇0∕𝜎

where 𝜎 is the conductivity. The conductivity of the ground near Gakona, Alaska, is approximately 3 mS/m,and for this simplified analysis we use an ionospheric conductivity of 0.09 mS/m at altitude h = 71.5 km forthe ionosphere, which we take to be the upper boundary of the waveguide. (As explained below, we believethat these values are the effective parameters for the observations.) Using these values, we obtain an aver-age quality factor of 55. The associated normalized resonant curves are shown in Figure 4 and show distinctamplitude peaks at exactly 2.1 kHz, 4.2 kHz, and 6.3 kHz.

For the expected characteristics of propagating modes we consider the TE and TM mode expressions withimaginary values of 𝛾 . We also include the effect of attenuation quantified by the attenuation constant 𝛼c foreach mode [Inan and Inan, 1999, pp. 276–277] given by

𝛼cTEM=

Rs

𝜂h; 𝛼cTEm

=Rs(fm∕f )2

𝜂h√

1 − (fm∕f )2; 𝛼cTMm

= 2Rs

𝜂h√

1 − (fm∕f )2(9)

Plots of the expected horizontal magnetic field magnitude for propagating modes up to third order (m = 3)are shown in Figure 5 for three distances corresponding to the relative locations of the VLF receivers. Equalexcitation of all modes has been assumed. The frequency dependence of the TE modes makes this plot ofpropagating waves also have peaks near multiples of 2 kHz, but these relative peaks can be seen to shift tohigher frequency for farther distances since attenuation for m> 0 modes is highest when f ≃ fm. Furthermore,the peaks from propagation are wider than those from resonance.

The above analytical analysis yields the expected frequency characteristic for purely resonant and purelypropagating modes. To examine the more realistic case of a combination of these phenomena, we also per-formed a finite difference time domain (FDTD) numerical simulation. This simulation takes into account theinhomogeneity but not anisotropy of the ionosphere using a scalar conductivity derived from Profile 2 inFigure 7 as the upper boundary of a parallel plate waveguide. The waveguide was excited by orthogonalhorizontal current densities of equal magnitude and phase in the x and y directions so that both TE and TMmodes would be equally excited. (More accurate current distributions in the heated region are discussed



0

0.5

1

0

0.5

1

0.92

0.94

0.96

0.98

1

Nor

mal

ized

Mag

nitu

de o

f Hor

izon

tal M

agne

tic F

ield

0 2 4 6 80

0.5

1

Frequency(kHz)

36km50km99km

All modes

TE modes only

TM modes only

TM0 (TEM) mode only

Figure 5. Normalized magnitude for propagating modes in the Earth-ionosphere parallel waveguide for differentpropagation distances assuming reflection at altitude of 71.5 km with ionospheric conductivity given by Profile 2 inFigure 7.

in section 4.) The source currents have a time-dependent differential Gaussian pulse with a half pulse width of60.735 μs giving broadband excitation over the 0.5–10 kHz band. Horizontal magnetic fields were calculatedat locations corresponding to the Chistochina, Paxson, and Paradise receivers. The magnitude as a function offrequency is shown in Figure 6. It is seen that similar to the analytical results, the peak of the field magnitudeshifts higher in frequency with distance from the source. For Paradise the second peak has shifted close to4.5 kHz and the third peak close to 7.1 kHz in agreement with the observations. The width of the peaks forParadise are also wider which is likewise in agreement with the observed frequency dependence near 4–6 kHzat Paradise.

We thus interpret the observations at Chistochina and Paxson to correspond primarily to local resonancemodes, while the observations at Paradise exhibit resonance behavior near 2 kHz and mostly propagatingcharacteristics above 3 kHz. It is reasonable to expect that the extent of a local vertical resonance in theEarth-ionosphere waveguide will be limited to the order of the size of the source and the wavelength in ques-tion. The ionospheric heated region above HAARP for a 2.75 MHz carrier has a diameter of approximately50 km when first-order side lobes are taken into account [Cohen, 2009]. The free space wavelengths for 2 kHz,4 kHz, and 6 kHz are 150 km, 75 km, and 50 km, respectively. Paradise is the most distant of the three sites(99 km versus 36 km and 52 km), so it is not surprising that the vertical resonances near 4 kHz and 6 kHz areless prominent at this site while the resonance near 2 kHz has a wavelength long enough to still be observed.Thus, for frequencies above 3 kHz the observations at Paradise clearly exhibit some characteristics of propa-gating waveguide modes, while the observations at Chistochina and Paxson exhibit mostly local resonancebehavior for frequencies even up to about 7 kHz. For the expected vertical resonance near 8 kHz, we see littleevidence of an amplitude peak at any of the sites. In the context of the expected enhancement or degradationof generated ELF/VLF waves from Earth-ionosphere waveguide effects, we see evidence that the transition



0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

Frequency (kHz)


Figure 6. FDTD simulation results showing magnitude as a function of frequency for ionospheric conductivity given byProfile 2 in Figure 7. The simulation is performed with 516 × 736 × 468 cells of size 0.2 km.

from enhancement at vertical resonances to degradation at the same valued mode cutoff frequencies occursat a distance of approximately one wavelength.3.1.2. Frequency Shift and Variability of Resonance PeaksClose examination of the specific frequencies of the multiple amplitude peaks observed at Chistochina andPaxson shows that the second and third resonances (4.3 kHz and 6.325 kHz) are not simple multiples of the first(2.1 kHz) as would be expected for a fixed spacing between two parallel conducting planes and as was seen inFigure 4. This departure from the ideal model can be partially explained by the fact that the reflection heightfor 1–10 kHz waves changes slightly with frequency. Analysis of the frequency-dependent reflection height isnontrivial and was investigated extensively in the 1960s and 1970s [Field and Engel, 1965; Bannister, 1979]. Wenote that some more contemporary published approaches like that of Ohya et al. [2003], who ignore the highcollision frequency in the D region, are not accurate in the ELF/VLF bands. Using the formulations providedby Field and Engel [1965] and Bannister [1979], the physical reflection height occurs where the conductioncurrent is equal to the displacement current or at an altitude z where

𝜔 =𝜔2

p(z)𝜈(z) cos(𝜃i)

(10)

and where 𝜈(z) is the altitude-dependent electron-neutral collision frequency,𝜔p(z) is the altitude-dependentplasma frequency, 𝜔 is the wave frequency, and 𝜃i is the incidence angle. To investigate vertical resonances,

4 5 6 7 8 9 10 11 1265

70

75

80

85

90

95

100

Figure 7. Four ionospheric D region profiles and electron-neutral collision frequency used to create Figure 8. Profile 1:winter night, Profile 2: summer night, Profile 3: winter day, and Profile 4: summer day [Cohen, 2009].



Figure 8. Expected reflection height as a function of frequency for four different ionospheric profiles and lengths of firstthree 𝜆∕2 multiples. Vertical resonances are expected to occur at the intersections of the curves. Observed amplitudepeaks for day and night are shown as squares and circles, respectively.

we take 𝜃i = 0. The electron density and collision frequency of four ionospheric profiles considered are pre-sented in Figure 7. Figure 8 shows the plot of reflection height as a function of frequency for those fourdifferent ionospheric profiles. The reflection height curves in Figure 8 can be seen to have a very moderatepositive slope implying that the reflection height increases slightly with frequency. Vertical resonances willoccur when the reflection height is an integer multiple of one half of a wavelength, 𝜆. The curves showing the𝜆∕2, 𝜆 and 3𝜆∕2 lengths as a function of frequency are also plotted in Figure 8, where the reflection heightand resonance curves intersect is the frequency of an expected resonance-induced amplitude enhancement.From the intersection points in Figure 8, we see that resonances at 2.125 kHz, 4.3 kHz, and 6.325 kHz areexpected for ionospheric Profile 3 and correspond to the observed magnitudes from 05:30 UT on 21 July (seeFigure 3a). The subauroral ionosphere over HAARP is of course variable, and this variability is also seen in theELF/VLF observations. If we analyze the observations from a single 5 min transmission at 8:40 UT on 21 July2011 (Figure 3b), we see observed resonances at 2.125 kHz, 4.1 kHz, and 6.1 kHz. These points are also plottedin Figure 8 and show that for this time Profile 2 is the best match to the data. The observed amplitude peaks areseen to be a function of the ionospheric profile, and the exact frequencies of peaks can potentially be used as aD region diagnostic.

3.1.3. Azimuthal Dependence of Observed AmplitudesTurning to the calibrated values of the observed magnitudes in Figure 3, it is clear that the highest waveamplitudes are observed at Chistochina. Second highest magnitudes are, in general, observed at Paradise,and the lowest wave amplitudes are generally observed at Paxson. Chistochina is the closest of the threesites to HAARP; therefore, it is not surprising that the highest wave amplitudes are observed there. Paxson islocated closer than Paradise to HAARP by almost 40 km, and therefore, the fact that the amplitudes generallyobserved at Paxson are lower than the amplitudes observed at Paradise suggests a significant azimuthaldependence of the radiation pattern. The ELF/VLF generation process involves modulation of both thePedersen and Hall components of the ionospheric conductivity tensor. The Hall currents are typically orientedalong the magnetic east-west direction (northwest-southeast geographic) with the Pedersen currents orthog-onal to this. For the altitudes of interest in this paper (< 80 km) magnitude of the Hall current is typicallya factor of 2 greater than the Pedersen current [Barr and Stubbe, 1984a, 1984b]. The analysis of polarizationeccentricity and numerical simulations discussed in the following sections provides evidence that observedELF/VLF waves at Chistochina and Paradise are sourced predominantly from the stronger Hall dipole whilethe waves at Paxson have components from both Hall and Pedersen currents.



Figure 9. The normalized polarization graphs of the magnetic field from the experiment over 5 min (5.30 UT–5.35 UT) on 21 July 2011 for the three sites,Chistochina (red), Paxson (green), and Paradise (blue).

3.2. PolarizationThe most general analysis of electromagnetic polarization takes into account both the direction and the rel-ative phasing of the field components. We follow the procedure of Gołkowski and Inan [2008] where theparameters of the polarization ellipse are calculated in the frequency domain from the complex signal f (t)synthesized from the two observed orthogonal components (NS(t), EW(t)) of the wave magnetic field

f (t) = NS(t) + iEW(t) (11)

The Fourier transform F(𝜔) of the above complex signal f (t) is calculated, and the positive and negativefrequency components can be written as follows

F(𝜔) = r+ei𝜃+ (12)

and

F(−𝜔) = r−ei𝜃− (13)

where r+, r−, and 𝜃+, 𝜃− are the amplitudes and phases of the positive and negative 𝜔, respectively, and alsothe right-hand and left-hand circularly polarized components of the signal. The geometry of the ellipse tracedout by the observed wave field vectors in the time domain is defined by the lengths of the semi major axis Aand the semi minor axis B and the angle 𝜙 measured from the geographic north-south direction. The relationbetween the ellipse parameters and F(𝜔) is as follows: 𝜙 is half of the difference between 𝜃+ and 𝜃− and the



0 1 2 3 4 5 6 7 8 90.4

0.5

0.6

0.7

0.8

0.9

1

Frequency(kHz)

Ecc

entr

icity

Observed Eccentricity vs Frequency


Figure 10. Eccentricity versus frequency averaged over 5 min (5.30 UT–5.35 UT) on 21 July 2011 for the three sites,Chistochina (red), Paxson (green), and Paradise (blue).

values of A and B are defined as A = r+ + r− and B = |r+ − r−|. The polarization ellipses obtained from theobserved magnetic field for the 40 different frequency tones at the three sites are depicted in Figure 9. Foreach polarization ellipse we also calculate the eccentricity as

Eccentricity =√

1 − B2∕A2 (14)

For linear polarization the eccentricity value is 1, and for pure circular polarization the eccentricity value is 0.

Figure 10 depicts the eccentricities observed at the three sites for the 40 frequency tones transmitted. Fromthe eccentricity curves it can be seen that waves observed at Paradise are predominantly linearly polarizedas compared to Paxson and Chistochina. Chistochina exhibits linear polarization for frequencies up to 5 kHzwith polarization becoming more elliptical at the higher frequencies. The ELF/VLF waves observed at Paxsonare the most elliptical of the three sites. The frequencies at which the waves observed at Paxson exhibit highlylinear polarization are limited to a narrow peak near 2 kHz and a broader peak between 3.8 kHz and 5.5 kHz. Webelieve that this is at least partly due to the vertical resonances described above that are prominent just above2 kHz and 4 kHz. The reason that linear polarization is expected to be observed at the resonance frequenciesis that reflection from the anisotropic ionosphere modifies the polarization of the generated signal. This canbe seen by calculating the reflection coefficient matrix that is a function of incident angle 𝜃i.

R(𝜃i) =[ ||R|| ||R⊥

⊥R|| ⊥R⊥

](15)

The elements of R give the ratio of reflected wave amplitude to incident wave amplitude for electric fieldorientation parallel and perpendicular to the plane of incidence. The off diagonal terms thus quantify theconversion from parallel to perpendicular polarization. Using the method described by Budden [1955], thereflection matrix for vertical incidence for Profile 2 for 4.2 kHz is calculated to be

R(𝜃i = 0) =[

0.8058 − 0.4843i −0.0682 − 0.0900i0.0690 + 0.0918i −0.9293 + 0.3193i

](16)

If we start with an initially circularly polarized wave, the amplitude and polarization after ionospheric reflectionis given by multiplication by R. Figure 11 shows the change in eccentricity that occurs after multiple reflec-tions from the ionosphere for both a single ray and the cumulative field from the sum of all the reflected rays.Figure 11 (inset) shows the corresponding polarization ellipse. The cumulative sum of multiple rays would onlybe observed for vertical resonances near the source. A single ionospheric reflection changes the polarizationfrom circular to elliptical; subsequent reflections make the polarization increase in linearity. The polarizationof the cumulative wave becomes highly linear after one reflection and retains a high eccentricity (> 0.9).Therefore, at the resonance frequencies, a standing wave pattern from the summation of multiple upward and



Figure 11. Change in eccentricity of an initially right-hand circularly polarized wave upon reflections from theionosphere described by Profile 2 in Figure 7. Dashed red trace shows eccentricity of an individual ray after undergoingmultiple vertical incident reflections. Solid blue trace is the eccentricity of the cumulative wave. Inset panel shows thenormalized polarization ellipse for the single ray and cumulative wave after each reflection.

downward propagating waves will yield a net linear polarization as is observed at the Paxson site. Consideredin isolation, this feature of the Paxson data is further evidence of the importance of the vertical resonancephenomena in the vicinity of the heated region. At the same time, at other frequencies including near 6.5 kHz,the propagating radiation from the ionospheric source region observed at Paxson exhibits elliptical polariza-tion can indicate the presence of two orthogonal current sources in phase quadrature. This effect is muchless pronounced at the other two sites. Modulated Hall and Pedersen are spatially orthogonal, but their rela-tive phase in time is more complicated. Barr and Stubbe [1984a] and Barr and Stubbe [1984b] found that thephase difference between modulated Hall and Pedersen currents to be either 0 or 180∘ depending on altitude.A phase difference of 90∘ would be necessary to generate circular polarization. In this context we note that themodulated currents are distributed over the heated region and additional phase differences can result frompropagation. We interpret the observations as indication of radiation at Chistochina and Paradise being dueto the dominant Hall dipole and the higher circularity observed at Paxson being due to contributions fromboth Hall and Pedersen currents.

4. Simulation of Ionospheric Current Modulation

In order to investigate the relationship between our observations and the modulated ionospheric sourcecurrents, we employ a numerical model of the ionospheric heating process. The modulation of ionosphericcurrents is modeled using HF ray tracing and collisional absorption providing the modified electron tem-perature as a function of time as has been done in other works [Tomko et al., 1980; Rodriguez and Inan,1994; Cohen et al., 2010b; Moore and Agrawal, 2011]. The modified electron temperature allows for calcu-lation of the modified Hall (𝜎H) and Pedersen (𝜎P) conductivities that are elements of the general plasmaconductivity tensor.

𝜎 =⎛⎜⎜⎝𝜎P −𝜎H 0𝜎H 𝜎P 00 0 𝜎||

⎞⎟⎟⎠ (17)



1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

0.8

1

1.2

1.4

FrequencyA

mpl

itude

(fT

)

Amplitude Vs Frequency from Perpendicular Currents


1 2 3 4 5 6 7 8 90.4

0.5

0.6

0.7

0.8

0.9

1

Frequency(kHz)

Ecc

entr

icity

Eccentricity Vs Frequency

ChistochinaPaxonParadise

(a)

(b)

Figure 12. (a) Amplitude versus frequency from the numerical model for selected frequencies. (b) Eccentricity versusfrequency from the numerical model.

The modified conductivities lead to induced currents by way of the electrojet electric field, E,

ΔJ = Δ𝜎 E (18)

where the electric field is taken as 10 mV/m and assumed to be static [Cohen et al., 2012] in the y direction cor-responding to magnetic north. The model assumes a stratified ionosphere in the altitude range from 49 km to100 km where the thickness of each layer is 1000 m. Once the currents are calculated, we derive the magneticfield radiated on the ground using the magnetic vector potential

B = ∇ × A (19)

The numerical model assumes a geomagnetic field in the z direction. A coordinate rotation is performed totake into account the magnetic zenith angle and declination at HAARP and then obtain the three componentsof the ELF/VLF magnetic field in geographic coordinates in the ground using

Bx = 2𝜇

4𝜋ΔVΣN

n=1

[Jyn

(z − zn) − Jzn(y − yn)

] 1 + jkR

R3e−jkR

By = 2𝜇

4𝜋ΔVΣN

n=1

[Jzn

(x − xn) − Jxn(z − zn)

] 1 + jkR

R3e−jkR



Figure 13. Polarization graphs from the numerical model for 12 selected frequencies.

Bz =𝜇

4𝜋ΔVΣN

n=1

[Jxn

(y − yn) − Jyn(x − xn)

] 1 + jkRR3

e−jkR = 0

R =√(x − xn)2 + (y − yn)2 + (z − zn)2

The presence of a conducting ground is taken into account using image theory.

We note that the numerical model takes into account only the HAARP-induced ionospheric ELF/VLF source.We do not attempt to model the propagation of the subsequent waves in the Earth-ionosphere waveguide,since our main goal is to assess the ionospheric source currents and how they determine the azimuthal depen-dence of the HAARP-induced ELF/VLF source. We thus do not expect to see features such as the vertical

Figure 14. Normalized magnetic field on the ground for modulation frequency of 6100 Hz due to Hall and Pedersenmodulated currents. Paxson is the only site where contribution of modulated Pedersen currents is greater thanmodulated Hall currents.



(a)

(b)

Figure 15. Simulated magnetic field magnitude on ground due to (a) perpendicular conductivities (Hall (𝜎H) andPedersen (𝜎P)) and due to (b) parallel conductivities (𝜎||.)resonance peaks in the simulated data. Figure 12 shows the simulated amplitude and eccentricity of polariza-tion as a function of frequency for 12 frequencies. Polarization ellipses for the simulated data can be seen inFigure 13. In terms of amplitudes, Chistochina shows the highest amplitudes as was seen in the data. For fre-quencies above 5 kHz, the amplitudes of Paradise exceed the amplitudes of Paxson. This effect was also seen inthe observations and confirms that, in general, higher amplitudes are radiated in the direction of northeasternazimuths as compared to northwestern azimuths. For polarization, the similarity between both observed andsimulated results is that fields at Chistochina and Paradise show higher linearity than the fields at Paxson.Polarization observed at Paxson is more circular as compared to the other sites, suggesting that the Paxsonreceiver observed fields radiated by both Hall and Pedersen currents and that the relative phase and loca-tion of these currents might be conducive to circular polarization. Figure 14 shows the contour plot of thenormalized simulated horizontal magnetic field strength due to Hall and Pedersen currents separately at eachsite for 6100 Hz. Only at Paxson is the contribution of the Pedersen current greater than that of the Hall current.The asymmetry of the patterns is due both to the magnetic declination (20.42∘) and also the magnetic zenithangle (15∘) as the oblique angle of the geomagnetic field affects both the modulated and image currents



1 2 3 4 5 6 7 8 91

2

3

4

5

6

7

8

FrequencyA

mpl

itude

(fT

)

Amplitude Vs Frequency with Parallel Currents


1 2 3 4 5 6 7 8 90.4

0.5

0.6

0.7

0.8

0.9

1

Frequency(kHz)

Ecc

entr

icity

Eccentricity Vs Frequency with Parallel Currents

ChistochinaPaxonParadise

(a)

(b)

Figure 16. (a) Amplitude and (b) eccentricity from the numerical model for selected frequencies for parallel conductivity(𝜎||) modulation.

in the model. We note that an additional potential anisotropy that is neglected here is the influence of thenonvertical geomagnetic field on the HF propagation.

4.1. Effect of Modulated Geomagnetically Aligned CurrentsThe numerical model considers only the modulation of Hall and Pedersen currents which are close to horizon-tal. There have been suggestions that observed ELF/VLF generated by ionospheric modification might alsoresult from so-called “loop back” currents, which are parallel to the geomagnetic field and arise in responsethe horizontal currents as a charge neutralization mechanism. In fact, it has been suggested that suchcurrents may, in fact, dominate the observed ELF/VLF within 100 km of the HAARP facility [Papadopoulos,2014]. It is important to keep in mind that the ambient parallel conductivity 𝜎|| is several orders of magnitudehigher than the other elements of the conductivity tensor. An ionospheric static electric field parallel tothe geomagnetic field is thus not physical, and for this reason our numerical code cannot simulate directmodulation of parallel, near vertical currents. Likewise, the model does not include strict enforcement ofthe continuity equation which is the basis of the loop back process [Payne, 2007]. Nevertheless, we can stilluse our model to investigate the expected effect of parallel currents on observations. A simulation was per-formed where only parallel currents were artificially input into the model of the same amplitude as the Hallcurrents in the earlier simulations. Figure 15 shows the magnitude of the observed magnetic field pattern onthe ground for the simulations with Hall and Pedersen currents as well as the artificial simulation with paral-lel currents only. In Figure 16 the frequency response and polarization of the artificial parallel only simulation



are shown. It can be seen that when only the parallel currents are taken into consideration, the simulationresults deviate from observations significantly. For example, in the observations, the Chistochina site has thehighest magnetic field amplitudes but the magnetic field generated due to the parallel currents yields ampli-tudes at Chistochina significantly lower than at the other two sites. Parallel currents are seen to generate aradiation null in the close vicinity of the HAARP facility, a feature that is not seen in our observations nor anyother published works. The polarization results from a “parallel only” simulation are also disparate from theobservations.

5. Summary and Discussion

Our key findings can be summarized as follows:

1. Lack of difference in ELF/VLF observations between O mode and X mode transmissions other than a sim-ple amplitude change confirms that collisional heating is the dominant process behind D region electrojetmodulation.

2. There is an azimuthal dependence to the HAARP-induced ELF/VLF source. Waves observed in the geo-graphic northwest azimuth have lower magnitudes and higher degree of circular polarization likely due tomore equal contribution of Hall and Pedersen currents. Other azimuths have radiation dominated by Hallcurrents.

3. Amplitude enhancements of observed ELF/VLF waves near multiples of 2 kHz are due to vertical resonancesbetween the Earth and the ionosphere. The exact frequencies of the resonances near 4 kHz and 6 kHz canbe used to diagnose the D region ionospheric profile.

4. The spatial extent of the vertical resonances is on the order of a wavelength; beyond this distance observedwaves show some characteristics of propagating waveguide modes.

5. Vertical geomagnetically aligned loop back currents play a negligible role in ELF/VLF observations on theground for the frequencies in the explored range (500 Hz–8.3 kHz).

In the context of the third point, we note that the D region ionosphere is notoriously difficult to probe directly.Gołkowski et al. [2013] recently proposed a ELF/VLF-driven D region diagnostic technique using dual HF beamsboth AM modulated but with a ELF phase offset. While the dual beam technique is attractive since it requiresobservations at only a single frequency, the requirement of two simultaneous HF beams is hard to realizeoutside of unique facilities like HAARP. On the other hand, identification of vertical resonance frequenciesrequires observations at closely spaced frequencies, but the single vertical HF beam configuration is readilyrealizable at other facilities including the Sura heater and the planned Arecibo heating facility. Experimentsat the latter in conjunction with the colocated powerful incoherent scatter radar will be the subject offuture study.

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AcknowledgmentsWe thank Ed Kennedy and the HAARPoperators for the opportunity to con-duct experiments during the 2011Student Summer Research Campaignat the HAARP facility. Former CUDenver students Matthew Webb andJason Carpenter assisted with data col-lection. Mark Gołkowski acknowledgessupport from National ScienceFoundation CAREER grant AGS1254365 to CU Denver. The transmis-sion formats used in this work can befound in the HAARP Summer 2011Campaign repository located at theurl: http://bagpipes.haarp.alaska.edu.The access to the data usedin this work will be providedupon request. The requestsfor data should be emailed to:[email protected],[email protected] [email protected].


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http://dx.doi.org/10.1002/jgra.50558

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